arXiv subjects
Publications and source records attributed to Larry Pileggi.
This work presents the design of AC line outage distribution factor created from the circuit-theoretic power flow models. Experiment results are shown to demonstrate its efficacy in quantifying the impact of line outages on the grid, and its resulting potential for fast contingency screening.
Given sensor readings over time from a power grid, how can we accurately detect when an anomaly occurs? A key part of achieving this goal is to use the network of power grid sensors to quickly detect, in real-time, when any unusual events, whether natural faults or malicious, occur on the power grid. Existing bad-data detectors in the industry lack the sophistication to robustly detect broad types of anomalies, especially those due to emerging cyber-attacks, since they operate on a single measurement snapshot of the grid at a time. New ML methods are more widely applicable, but generally do not consider the impact of topology change on sensor measurements and thus cannot accommodate regular topology adjustments in historical data. Hence, we propose DYNWATCH, a domain knowledge based and topology-aware algorithm for anomaly detection using sensors placed on a dynamic grid. Our approach is accurate, outperforming existing approaches by 20% or more (F-measure) in experiments; and fast, running in less than 1.7ms on average per time tick per sensor on a 60K+ branch case using a laptop computer, and scaling linearly in the size of the graph.
The utility of domain-specific knowledge for modeling, simulation, and optimization has been demonstrated for various research problem domains, including power systems. The concept of Equivalent Circuit Programming was previously developed and facilitated for robust, efficient, and scalable solution of network simulation and optimization problems. This paper extends the theoretical foundation of Equivalent Circuit Programming to enable the fusion of optimization theory and algorithms with the numerical methods that utilize the domain-specific knowledge of power flow models. The generality, scalability, and numerical robustness of the resulting framework are demonstrated on realistic AC power flow (ACPF) models of up to 70k buses with proper enforcement of industry-required operational and security constraints.
In recent years, the ML community has seen surges of interest in both adversarially robust learning and implicit layers, but connections between these two areas have seldom been explored. In this work, we combine innovations from these areas to tackle the problem of N-k security-constrained optimal power flow (SCOPF). N-k SCOPF is a core problem for the operation of electrical grids, and aims to schedule power generation in a manner that is robust to potentially k simultaneous equipment outages. Inspired by methods in adversarially robust training, we frame N-k SCOPF as a minimax optimization problem - viewing power generation settings as adjustable parameters and equipment outages as (adversarial) attacks - and solve this problem via gradient-based techniques. The loss function of this minimax problem involves resolving implicit equations representing grid physics and operational decisions, which we differentiate through via the implicit function theorem. We demonstrate the efficacy of our framework in solving N-3 SCOPF, which has traditionally been considered as prohibitively expensive to solve given that the problem size depends combinatorially on the number of potential outages.
Alternating-Current Optimal Power Flow (AC-OPF) is an optimization problem critical for planning and operating the power grid. The problem is traditionally formulated using only continuous variables. Typically, control devices with discrete-valued settings, which provide valuable flexibility to the network and improve resilience, are omitted from AC-OPF formulations due to the difficulty of integrality constraints. We propose a two-stage homotopy algorithm to solve the AC-OPF problem with discrete-valued control settings. This method does not rely on prior knowledge of control settings or other initial conditions. The first stage relaxes the discrete settings to continuous variables and solves the optimization using a robust homotopy technique. Once the solution has been obtained using relaxed models, second homotopy problem gradually transforms the relaxed settings to their nearest feasible discrete values. We test the proposed algorithm on several large networks with switched shunts and adjustable transformers and show it can outperform a similar state-of-the-art solver.
Proliferation of grid resources on the distribution network along with the inability to forecast them accurately will render the existing methodology of grid operation and control untenable in the future. Instead, a more distributed yet coordinated approach for grid operation and control will emerge that models and analyzes the grid with a larger footprint and deeper hierarchy to unify control of disparate T&D grid resources under a common framework. Such approach will require AC state-estimation (ACSE) of joint T&D networks. Today, no practical method for realizing combined T&D ACSE exists. This paper addresses that gap from circuit-theoretic perspective through realizing a combined T&D ACSE solution methodology that is fast, convex and robust against bad-data. To address daunting challenges of problem size (million+ variables) and data-privacy, the approach is distributed both in memory and computing resources. To ensure timely convergence, the approach constructs a distributed circuit model for combined T&D networks and utilizes node-tearing techniques for efficient parallelism. To demonstrate the efficacy of the approach, combined T&D ACSE algorithm is run on large test networks that comprise of multiple T&D feeders. The results reflect the accuracy of the estimates in terms of root mean-square error and algorithm scalability in terms of wall-clock time.
Quantifying the impact of inverter-based distributed generation (DG) sources on power-flow distribution system cases is arduous. Existing distribution system tools predominately model distributed generation sources as either negative PQ loads or as a PV generator and then employed a PV-PQ switching algorithm to mimic Volt/VAR support. These models neglect the unique characteristics of inverter-based distributed generation sources, have scalability and convergence issues, and are ill-suited for increasing solar penetration scenarios. This work proposes an inverter-based DG model accounting for the inverter's topology, sensing position, and control strategies. The model extends recently introduced analytical positive sequence generator models for three-phase studies. The use of circuit-simulation based heuristics help achieve robust convergence. Simulation of the PG&E prototypical feeders using a prototype solver demonstrate the model's accuracy and efficacy.
Fast and accurate optimization and simulation is widely becoming a necessity for large scale transmission resiliency and planning studies such as N-1 SCOPF, batch contingency solvers, and stochastic power flow. Current commercial tools, however, prioritize speed of convergence over accuracy by relying on initial conditions that are taken from the steady state solution of similar network configurations that are not guaranteed to lie within a convex region of a valid solution. In this paper we introduce a globally convergent algorithm to facilitate fast and accurate AC steady state simulation and optimization based on prior knowledge from similar networks. The approach uses a homotopy method that gradually and efficiently translates a previously known network configuration to the current network configuration. The proposed formulation is highly scalable, and its efficacy is demonstrated for resiliency study and optimization of large networks up to 70k buses.
For reliable and secure power grid operation, AC state-estimation (ACSE) must provide certain guarantees of convergence while being resilient against bad-data. This paper develops a circuit-theoretic weighted least absolute value (WLAV) based hybrid ACSE that satisfies these needs to overcome some of the limitations of existing ACSE methods. Hybrid refers to the inclusion of RTU and PMU measurement data, and the use of the LAV objective function enables automatic rejection of bad data while providing clear identification of suspicious measurements from the sparse residual vector. Taking advantage of linear construction of the measurement models in circuit-theoretic approach, the proposed hybrid SE is formulated as a LP problem with guaranteed convergence. To address efficiency, we further develop problem-specific heuristics for fast convergence. To validate the efficacy of the proposed approach, we run ACSE on large cases and compare the results against WLS-based algorithms. We further demonstrate the advantages of our solution methodology over standard commercial LP solvers through comparison of runtime and convergence performance.
Alternating-Current Optimal Power Flow (AC-OPF) is framed as a NP-hard non-convex optimization problem that solves for the most economical dispatch of grid generation given the AC-network and device constraints. Although there are no standard methodologies for obtaining the global optimum for the problem, there is considerable interest from planning and operational engineers in finding a local optimum. Nonetheless, solving for the local optima of a large AC-OPF problem is challenging and time-intensive, as none of the leading non-linear optimization toolboxes can provide any timely guarantees of convergence. To provide robust local convergence for large complex systems, we introduce a homotopy-based approach that solves a sequence of primal-dual interior point problems. We utilize the physics of the grid to develop the proposed homotopy method and demonstrate the efficacy of this approach on U.S. Eastern Interconnection sized test networks.
Traditional state estimation (SE) methods that are based on nonlinear minimization of the sum of localized measurement error functionals are known to suffer from non-convergence and large residual errors. In this paper we propose an equivalent circuit formulation (ECF)-based SE approach that inherently considers the complete network topology and associated physical constraints. We analyze the mathematical differences between the two approaches and show that our approach produces a linear state-estimator that is mathematically a quadratic programming (QP) problem with closed-form solution. Furthermore, this formulation imposes additional topology-based constraints that provably shrink the feasible region and promote convergence to a more physically meaningful solution. From a probabilistic viewpoint, we show that our method applies prior knowledge into the estimate, thus converging to a more physics-based estimate than the traditional observation-driven maximum likelihood estimator (MLE). Importantly, incorporation of the entire system topology and underlying physics, while being linear, makes ECF-based SE advantageous for large-scale systems.
Secure and fast grid restoration from a collapsed state is increasingly critical as blackouts are becoming more prevalent around the globe. Generally, the restoration of grid during a blackout is achieved with the help of Supervisory Control and Data Acquisition System (SCADA) based central control; however, with the threat of cyber-blackouts, this presumption of an available and secure SCADA system is not valid. This is also true for grids in developing countries as well as for many distribution and micro grids that lack SCADA. In this paper, we introduce an online framework for localized grid restoration that validates and updates a pre-defined crank path in real-time based on the vital grid states of voltages, currents and frequency. The proposed framework maintains an online network topology of the localized grid that can continuously sample local measurements and update the grid model, thereby circumventing SCADA based central control. In the results section we demonstrate the efficacy of this framework for blackstart by ensuring a feasible crank path with voltage and frequency states within bounds, while further assisting in synchronization of two disconnected sub-grids during the re-energization process using a distributed framework.
Recent development of techniques that improve the convergence properties of power flow simulation have been demonstrated to facilitate scaling to large system sizes (80k+ buses). However, the problem remains to reliably identify cases that are infeasible, system configurations that have no solution. In this paper, we use the circuit theoretic approach based on adjoint networks to evaluate the feasibility of a power flow test case and further locate and quantify the source of infeasibility in the cases operating beyond the tip of the nose curve. By creating infeasibility current source models that are added to each node of the system model and further coupling each source to its corresponding node of the adjoint network, any locations of insufficient real or reactive power are captured by a non-zero response of the adjoint network. Furthermore, it is shown that the proposed joint simulation of power flow and its adjoint network models provide the optimally minimized currents that can be later utilized to inform corrective actions to restore the feasibility of power flow problems.
Simulating potential cascading failures can be useful for avoiding or mitigating such events. Currently, existing steady-state analysis tools are ill-suited for simulating cascading outages as they do not model frequency dependencies, they require good initial conditions to converge, and they are unable to distinguish between a collapsed grid state from a hard-to-solve test case. In this paper, we extend a circuit-theoretic approach for simulating the steady-state of a power grid to incorporate frequency deviations and implicit models for underfrequency and undervoltage load shedding. Using these models, we introduce a framework capable of robustly solving cascading outages of large-scale systems that can also locate infeasible regions. We demonstrate the efficacy of our approach by simulating entire cascading outages on more than 8000 nodes sample testcase.
A method is proposed to identify and localize the cause of network collapse with augmented power flow analysis for a grid model with insufficient resources. Owing to heavy network loading, insufficient generation, component failures and unavoidable disturbances, power grid models can sometimes fail to converge to a feasible solution for a steady-state power flow study. For applications such as system expansion planning, it is desirable to locate the system buses that are contributing to network infeasibilities to facilitate corrective actions. This paper proposes a novel LASSO-inspired regularization of the power flow matrix that enforces sparsity to localize and quantify infeasibilities in the network. One of the examples demonstrates how the proposed method is capable of localizing a source of blackout to a single dominant bus on an 80k+ bus eastern interconnection model.
In this paper, we extend a circuit-based, current-voltage power flow formulation to include frequency deviations and implicitly model generator primary and secondary control actions as a function of their temporal dependence. This includes extending the slack bus generator model(s) to better represents its true behavior with frequency controls. These implicit models obviate the need for outer iteration loops and improve the robustness of the simulation convergence when frequency deviations are considered. The simulation framework is highly scalable and is demonstrated on 85k+ bus systems.
The future electric grid will consist of significant penetration of renewable and distributed generation that is likely to create a homogenous transmission and distribution (T&D) system, requiring tools that can model and robustly simulate the combined T&D networks. Existing tools use disparate models and formulations for simulation of transmission versus distribution grids and solving for the steady-state solution of the combined T&D networks often lacks convergence robustness and scalability to large systems. In this paper, we show that modeling both the T&D grid elements in terms of currents and voltages using an equivalent circuit framework enables simulation of combined positive sequence networks of the transmission grids with three-phase networks of the distribution grids without loss of generality. We further demonstrate that we can ensure robust convergence for these resulting large-scale complex T&D systems when the circuit simulation methods are applied to them. Our results illustrate robust convergence of combined T&D networks using a direct Newton-Raphson solver on a single machine for smaller sized systems and using a parallel Gauss-Seidel-Newton solver on multiple machines for larger sized systems with greater than million nodes.
The equivalent split-circuit formulation is a novel approach that has recently been applied to a range of power system related problems. As a result, a linear and a nonlinear method for power system state estimation with simultaneous treatment of the conventional and synchrophasor measurements have been proposed. In this paper, new circuit models are introduced for different combinations of conventional measurements, thus providing a complete modelling framework for these methods. Additionally, handling cases of null injections and buses with no measurements are included. Simulations are performed on several test systems in order to evaluate the performance of both methods with the enhanced modelling framework and to compare them to a hybrid constrained estimator based on the conventional WLS approach.